Shape transformations in optically trapped particles and minimal surfaces: An experimental and theoretical study

Optical tweezing can be used to isolate single, micrometre sized particles. This is facilitated by a gradient force from a tightly focussed laser beam. The optical tweezing microscope at the University of Leicester has been integrated with instrumentation for spectroscopic detection. In this work, both elastic and inelastic light scattering techniques are used to monitor physical changes in lipid vesicles and liquid aerosol droplets. Alongside this experimental work, numerical methods and mathematical models have been used to produce images of the coalescence of liquid droplets. The goal of this project was to refine mathematical models for shape transformations in microparticles and further develop elastic light scattering techniques. Individual unilamellar vesicles have been optically trapped and, by measuring the intensity modulation of elastic back scattered light, changes in the biophysical properties of lipid bilayers were revealed. Our approach offers unprecedented temporal resolution and, uniquely, physical transformations of lipid bilayers can be monitored on a length scale of micrometers. As an example, the deformation of a membrane bilayer following the gel to fluid phase transition in a pure phospholipid vesicle was observed to take place across an interval of 54 ± 5 ms. The binary coalescence of liquid microdroplets is investigated by both experimental and computational methods in chapter 6. Different theoretical models are explored for simulating the shape transformations occurring during aerosol droplet coalescence. A finite element model was identified as most suitable for precisely mapping the morphological changes. This model was then compared to experimental recordings of elastic light scattering over a coalescence, for droplets of different viscosity and coalescence trajectory. The visualization software was explored further in an investigation of shape transformations of minimal surfaces. By expressing a minimal surface as the real part of a holomorphic function, the surface may be transformed to create new families of minimal surfaces. In chapter 7 these transformations are applied to the minimal surface known as the k-noid. The properties of the resulting surfaces are then investigated.